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Surface formula identification

  1. May 7, 2007 #1
    1. The problem statement, all variables and given/known data

    Identify the surface given by the equation 4x^2 +4y^2 −8y −z^2 = 0.

    2. Relevant equations

    x^2/c^2 + y^2/c^2 - z^2/c^2 = 1

    (textbook definition for hyperboloid of one sheet.

    3. The attempt at a solution

    I know just by looking at the textbook formula what surface this is. However, my professor gives the following answer for the problem..

    It is a hyperboloid of one sheet, x^2 + y^2 − z2/2^2 = 1

    I get what the surface is, I just don't understand how he algebraically changed the formula to the above solution..

    is (4x^2 +4y^2 −8y −z^2 = 0 ) the same as (x^2 + y^2 − z2/2^2 = 1)?

    thanks. :)
  2. jcsd
  3. May 7, 2007 #2


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    Homework Helper

    complete the square on the y term.
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